Subgroups — C₆₇×#34461 #30713712

Order 17152.

2368 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#553×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2383	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2376	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2370	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2361	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2361	C₂	1	1	yes	maximal, characteristic, complemented
8	D₄×C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×C₄⋊C₄×C₆₇	C₂	1	2	yes	maximal, complemented
10	D₄×C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2347	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2345	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2334	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2330	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2325	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2324	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2322	C₂	1	2	yes	maximal, complemented
18	C₆₇×#2319	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2318	C₂	1	2	yes	maximal, complemented
20	C₆₇×#2317	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#389×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2290	C₂	1	1	yes	maximal, characteristic, complemented
24	#553×C₆₇	C₄	1	16	yes	complemented
25	C₂×#126×C₆₇	C₂²	1	2	yes	—
26	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#123×C₆₇	C₂²	1	2	yes	—
28	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×#121×C₆₇	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
39	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
42	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
43	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
45	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
46	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
47	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
48	#390×C₆₇	C₂²	1	1	yes	characteristic
49	#390×C₆₇	C₂²	1	1	yes	characteristic
50	#390×C₆₇	C₂²	1	2	yes	—
51	#389×C₆₇	C₂²	1	1	yes	characteristic
52	#389×C₆₇	C₂²	1	2	yes	—
53	#389×C₆₇	C₂²	1	1	yes	characteristic
54	#389×C₆₇	C₂²	1	1	yes	characteristic
55	#389×C₆₇	C₂²	1	1	yes	characteristic
56	#389×C₆₇	C₂²	1	2	yes	—
57	#389×C₆₇	C₂²	1	1	yes	characteristic
58	#389×C₆₇	C₂²	1	1	yes	characteristic
59	#389×C₆₇	C₂²	1	1	yes	characteristic
60	#389×C₆₇	C₂²	1	1	yes	characteristic
61	#389×C₆₇	C₂²	1	2	yes	—
62	#389×C₆₇	C₂²	1	2	yes	—
63	#389×C₆₇	C₂²	1	2	yes	—
64	#389×C₆₇	C₂²	1	2	yes	—
65	#388×C₆₇	C₂²	1	1	yes	characteristic
66	#388×C₆₇	C₂²	1	1	yes	characteristic
67	#388×C₆₇	C₂²	1	2	yes	—
68	#388×C₆₇	C₂²	1	2	yes	—
69	#388×C₆₇	C₂²	1	2	yes	—
70	#388×C₆₇	C₂²	1	2	yes	—
71	#388×C₆₇	C₂²	1	2	yes	—
72	#388×C₆₇	C₂²	1	2	yes	—
73	#388×C₆₇	C₂²	1	2	yes	—
74	#388×C₆₇	C₂²	1	2	yes	—
75	#387×C₆₇	C₂²	1	1	yes	characteristic
76	#387×C₆₇	C₂²	1	1	yes	characteristic
77	#387×C₆₇	C₂²	1	2	yes	—
78	#387×C₆₇	C₂²	1	2	yes	—
79	#387×C₆₇	C₂²	1	2	yes	—
80	#387×C₆₇	C₂²	1	2	yes	—
81	#387×C₆₇	C₂²	1	2	yes	—
82	#387×C₆₇	C₂²	1	2	yes	—
83	#386×C₆₇	C₂²	1	1	yes	characteristic
84	#386×C₆₇	C₂²	1	1	yes	characteristic
85	#386×C₆₇	C₂²	1	2	yes	—
86	#386×C₆₇	C₂²	1	2	yes	—
87	#386×C₆₇	C₂²	1	2	yes	—
88	#386×C₆₇	C₂²	1	2	yes	—
89	#385×C₆₇	C₂²	1	1	yes	characteristic
90	#385×C₆₇	C₂²	1	1	yes	characteristic
91	#385×C₆₇	C₂²	1	2	yes	—
92	#385×C₆₇	C₂²	1	2	yes	—
93	#385×C₆₇	C₂²	1	2	yes	—
94	#385×C₆₇	C₂²	1	2	yes	—
95	#385×C₆₇	C₂²	1	2	yes	—
96	#385×C₆₇	C₂²	1	2	yes	—
97	#385×C₆₇	C₂²	1	2	yes	—
98	#385×C₆₇	C₂²	1	2	yes	—
99	#385×C₆₇	C₂²	1	2	yes	—
100	#384×C₆₇	C₂²	1	2	yes	—
101	#384×C₆₇	C₂²	1	1	yes	characteristic
102	#383×C₆₇	C₂²	1	2	yes	—
103	#382×C₆₇	C₂²	1	2	yes	—
104	#381×C₆₇	C₂²	1	2	yes	—
105	#380×C₆₇	C₂²	1	1	yes	characteristic
106	#380×C₆₇	C₂²	1	2	yes	—
107	#380×C₆₇	C₂²	1	2	yes	—
108	#380×C₆₇	C₂²	1	1	yes	characteristic
109	#380×C₆₇	C₂²	1	2	yes	—
110	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
117	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
120	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
121	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
122	#376×C₆₇	C₂²	1	1	yes	characteristic
123	C₂×#95×C₆₇	C₂²	1	2	yes	—
124	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
125	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
128	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
133	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
134	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
135	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
136	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
137	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
138	#126×C₆₇	C₂×C₄	1	16	yes	complemented
139	#125×C₆₇	C₂×C₄	1	8	yes	complemented
140	#123×C₆₇	C₂×C₄	1	16	yes	complemented
141	#121×C₆₇	C₂×C₄	1	16	yes	complemented
142	#121×C₆₇	C₂×C₄	1	8	yes	complemented
143	#121×C₆₇	C₂×C₄	1	8	yes	complemented
144	C₄×D₄×C₆₇	—	4	2	no	—
145	C₄×D₄×C₆₇	—	4	2	no	—
146	C₄×D₄×C₆₇	—	4	4	no	—
147	C₄×D₄×C₆₇	—	4	4	no	—
148	C₄×D₄×C₆₇	—	4	4	no	—
149	C₄×D₄×C₆₇	—	4	4	no	—
150	C₄×D₄×C₆₇	C₂×C₄	1	16	yes	complemented
151	C₄×D₄×C₆₇	C₂×C₄	1	8	yes	complemented
152	C₄×D₄×C₆₇	C₂×C₄	1	8	yes	complemented
153	#117×C₆₇	—	4	2	no	—
154	#117×C₆₇	C₂×C₄	1	8	yes	complemented
155	C₂×C₄⋊C₄×C₆₇	—	4	4	no	—
156	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
157	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
158	C₂×C₄⋊C₄×C₆₇	—	4	4	no	—
159	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	8	yes	complemented
160	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
164	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
185	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
189	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
190	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
191	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
192	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
193	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
207	C₂×C₄²×C₆₇	—	4	2	no	—
208	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
215	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
216	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
217	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
218	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
219	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
220	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
221	#95×C₆₇	C₂³	1	2	yes	—
222	#95×C₆₇	C₂³	1	2	yes	—
223	#95×C₆₇	C₂³	1	2	yes	—
224	#95×C₆₇	C₂³	1	2	yes	—
225	#95×C₆₇	C₂³	1	1	yes	characteristic
226	#95×C₆₇	C₂³	1	1	yes	characteristic
227	#95×C₆₇	C₂³	1	1	yes	characteristic
228	#95×C₆₇	C₂³	1	1	yes	characteristic
229	#95×C₆₇	C₂³	1	1	yes	characteristic
230	#95×C₆₇	C₂³	1	2	yes	—
231	#95×C₆₇	C₂³	1	2	yes	—
232	#95×C₆₇	C₂³	1	2	yes	—
233	#95×C₆₇	C₂³	1	2	yes	—
234	#95×C₆₇	C₂³	1	1	yes	characteristic
235	#95×C₆₇	C₂³	1	1	yes	characteristic
236	#95×C₆₇	C₂³	1	1	yes	characteristic
237	#95×C₆₇	C₂³	1	1	yes	characteristic
238	#95×C₆₇	C₂³	1	2	yes	—
239	#95×C₆₇	C₂³	1	2	yes	—
240	#95×C₆₇	C₂³	1	2	yes	—
241	#95×C₆₇	C₂³	1	2	yes	—
242	#95×C₆₇	C₂³	1	2	yes	—
243	#95×C₆₇	C₂³	1	2	yes	—
244	#95×C₆₇	C₂³	1	2	yes	—
245	#95×C₆₇	C₂³	1	1	yes	characteristic
246	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
247	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
248	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
249	C₂×D₄×C₆₇	—	2	4	no	—
250	C₂×D₄×C₆₇	—	2	2	no	—
251	C₂×D₄×C₆₇	—	2	4	no	—
252	C₂×D₄×C₆₇	—	2	2	no	—
253	C₂×D₄×C₆₇	—	2	2	no	—
254	C₂×D₄×C₆₇	—	2	2	no	—
255	C₂×D₄×C₆₇	—	4	2	no	—
256	C₂×D₄×C₆₇	—	4	2	no	—
257	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
258	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
259	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
260	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
261	C₂²×C₄×C₆₇	—	2	2	no	—
262	C₂²×C₄×C₆₇	—	2	2	no	—
263	C₂²×C₄×C₆₇	—	2	2	no	—
264	C₂²×C₄×C₆₇	—	2	2	no	—
265	C₂²×C₄×C₆₇	—	2	2	no	—
266	C₂²×C₄×C₆₇	—	2	2	no	—
267	C₂²×C₄×C₆₇	—	2	4	no	—
268	C₂²×C₄×C₆₇	—	2	2	no	—
269	C₂²×C₄×C₆₇	—	2	4	no	—
270	C₂²×C₄×C₆₇	—	4	1	no	—
271	C₂²×C₄×C₆₇	—	4	1	no	—
272	C₂²×C₄×C₆₇	—	4	2	no	—
273	C₂²×C₄×C₆₇	—	4	2	no	—
274	C₂²×C₄×C₆₇	—	4	2	no	—
275	C₂²×C₄×C₆₇	—	4	2	no	—
276	C₂²×C₄×C₆₇	—	4	1	no	—
277	C₂²×C₄×C₆₇	—	4	2	no	—
278	C₂²×C₄×C₆₇	—	4	2	no	—
279	C₂²×C₄×C₆₇	—	4	2	no	—
280	C₂²×C₄×C₆₇	—	4	2	no	—
281	C₂²×C₄×C₆₇	—	4	2	no	—
282	C₂²×C₄×C₆₇	—	4	2	no	—
283	C₂²×C₄×C₆₇	—	4	2	no	—
284	C₂²×C₄×C₆₇	—	4	2	no	—
285	C₂²×C₄×C₆₇	—	4	2	no	—
286	C₂²×C₄×C₆₇	—	4	2	no	—
287	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
288	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
289	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
290	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
291	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
307	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
308	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
311	C₄⋊C₄×C₆₇	—	2	2	no	—
312	C₄⋊C₄×C₆₇	—	2	4	no	—
313	C₄⋊C₄×C₆₇	—	2	2	no	—
314	C₄⋊C₄×C₆₇	—	2	4	no	—
315	C₄⋊C₄×C₆₇	—	2	2	no	—
316	C₄⋊C₄×C₆₇	—	2	2	no	—
317	C₄⋊C₄×C₆₇	—	2	2	no	—
318	C₄⋊C₄×C₆₇	—	4	2	no	—
319	C₄⋊C₄×C₆₇	—	4	2	no	—
320	C₄⋊C₄×C₆₇	—	4	2	no	—
321	C₄⋊C₄×C₆₇	—	4	2	no	—
322	C₄⋊C₄×C₆₇	—	4	2	no	—
323	C₄⋊C₄×C₆₇	—	4	2	no	—
324	C₄⋊C₄×C₆₇	—	4	1	no	—
325	C₄⋊C₄×C₆₇	—	4	2	no	—
326	C₄⋊C₄×C₆₇	—	4	1	no	—
327	C₄⋊C₄×C₆₇	—	4	1	no	—
328	C₄⋊C₄×C₆₇	—	4	2	no	—
329	C₄⋊C₄×C₆₇	—	4	2	no	—
330	C₄⋊C₄×C₆₇	—	4	2	no	—
331	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
332	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
333	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
334	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
335	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
336	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
337	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
338	C₂²⋊C₄×C₆₇	—	2	4	no	—
339	C₂²⋊C₄×C₆₇	—	2	2	no	—
340	C₂²⋊C₄×C₆₇	—	2	2	no	—
341	C₂²⋊C₄×C₆₇	—	2	2	no	—
342	C₂²⋊C₄×C₆₇	—	4	2	no	—
343	C₂²⋊C₄×C₆₇	—	4	1	no	—
344	C₂²⋊C₄×C₆₇	—	4	1	no	—
345	C₂²⋊C₄×C₆₇	—	4	1	no	—
346	C₂²⋊C₄×C₆₇	—	4	2	no	—
347	C₂²⋊C₄×C₆₇	—	4	2	no	—
348	C₂²⋊C₄×C₆₇	—	4	2	no	—
349	C₂²⋊C₄×C₆₇	—	4	2	no	—
350	C₂²⋊C₄×C₆₇	—	4	2	no	—
351	C₂²⋊C₄×C₆₇	—	4	2	no	—
352	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
353	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
354	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
355	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
356	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
357	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
358	C₄²×C₆₇	—	2	2	no	—
359	C₄²×C₆₇	—	2	2	no	—
360	C₄²×C₆₇	—	2	2	no	—
361	C₄²×C₆₇	—	2	2	no	—
362	C₄²×C₆₇	—	4	1	no	—
363	C₄²×C₆₇	—	4	1	no	—
364	C₄²×C₆₇	—	4	2	no	—
365	C₄²×C₆₇	—	4	2	no	—
366	C₄²×C₆₇	—	4	2	no	—
367	C₄²×C₆₇	—	4	2	no	—
368	C₄²×C₆₇	—	4	2	no	—
369	C₄²×C₆₇	C₂²×C₄	1	8	yes	—
370	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
371	C₂³×C₆₇	—	2	1	no	—
372	C₂³×C₆₇	—	2	1	no	—
373	C₂³×C₆₇	—	2	1	no	—
374	C₂³×C₆₇	—	2	1	no	—
375	C₂³×C₆₇	—	2	1	no	—
376	C₂³×C₆₇	—	2	1	no	—
377	C₂³×C₆₇	—	2	2	no	—
378	C₂³×C₆₇	—	2	2	no	—
379	C₂³×C₆₇	—	2	1	no	—
380	C₂³×C₆₇	—	2	2	no	—
381	C₂³×C₆₇	—	2	1	no	—
382	C₂³×C₆₇	—	2	1	no	—
383	C₂³×C₆₇	—	2	2	no	—
384	C₂³×C₆₇	—	2	2	no	—
385	C₂³×C₆₇	—	2	2	no	—
386	C₂³×C₆₇	—	2	1	no	—
387	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
388	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
389	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
390	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
391	C₂³×C₆₇	2₋¹⁺⁴	1	2	yes	—
392	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
393	D₄×C₆₇	—	2	16	no	—
394	D₄×C₆₇	—	2	8	no	—
395	D₄×C₆₇	—	2	8	no	—
396	D₄×C₆₇	—	4	8	no	—
397	C₂×C₄×C₆₇	—	2	1	no	—
398	C₂×C₄×C₆₇	—	2	1	no	—
399	C₂×C₄×C₆₇	—	2	2	no	—
400	C₂×C₄×C₆₇	—	2	1	no	—
401	C₂×C₄×C₆₇	—	2	1	no	—
402	C₂×C₄×C₆₇	—	2	2	no	—
403	C₂×C₄×C₆₇	—	2	1	no	—
404	C₂×C₄×C₆₇	—	2	2	no	—
405	C₂×C₄×C₆₇	—	2	1	no	—
406	C₂×C₄×C₆₇	—	2	1	no	—
407	C₂×C₄×C₆₇	—	2	1	no	—
408	C₂×C₄×C₆₇	—	2	2	no	—
409	C₂×C₄×C₆₇	—	2	1	no	—
410	C₂×C₄×C₆₇	—	2	2	no	—
411	C₂×C₄×C₆₇	—	2	1	no	—
412	C₂×C₄×C₆₇	—	2	2	no	—
413	C₂×C₄×C₆₇	—	2	8	no	—
414	C₂×C₄×C₆₇	—	2	8	no	—
415	C₂×C₄×C₆₇	—	2	1	no	—
416	C₂×C₄×C₆₇	—	2	1	no	—
417	C₂×C₄×C₆₇	—	2	1	no	—
418	C₂×C₄×C₆₇	—	2	1	no	—
419	C₂×C₄×C₆₇	—	2	1	no	—
420	C₂×C₄×C₆₇	—	2	1	no	—
421	C₂×C₄×C₆₇	—	2	1	no	—
422	C₂×C₄×C₆₇	—	2	2	no	—
423	C₂×C₄×C₆₇	—	2	2	no	—
424	C₂×C₄×C₆₇	—	2	2	no	—
425	C₂×C₄×C₆₇	—	2	2	no	—
426	C₂×C₄×C₆₇	—	2	1	no	—
427	C₂×C₄×C₆₇	—	2	2	no	—
428	C₂×C₄×C₆₇	—	2	1	no	—
429	C₂×C₄×C₆₇	—	2	2	no	—
430	C₂×C₄×C₆₇	—	2	2	no	—
431	C₂×C₄×C₆₇	—	2	2	no	—
432	C₂×C₄×C₆₇	—	2	2	no	—
433	C₂×C₄×C₆₇	—	2	1	no	—
434	C₂×C₄×C₆₇	—	2	2	no	—
435	C₂×C₄×C₆₇	—	2	1	no	—
436	C₂×C₄×C₆₇	—	2	1	no	—
437	C₂×C₄×C₆₇	—	2	1	no	—
438	C₂×C₄×C₆₇	—	2	1	no	—
439	C₂×C₄×C₆₇	—	2	1	no	—
440	C₂×C₄×C₆₇	—	2	2	no	—
441	C₂×C₄×C₆₇	—	2	1	no	—
442	C₂×C₄×C₆₇	—	2	1	no	—
443	C₂×C₄×C₆₇	—	2	1	no	—
444	C₂×C₄×C₆₇	—	2	2	no	—
445	C₂×C₄×C₆₇	—	2	1	no	—
446	C₂×C₄×C₆₇	—	2	1	no	—
447	C₂×C₄×C₆₇	—	2	1	no	—
448	C₂×C₄×C₆₇	—	4	8	no	—
449	C₂×C₄×C₆₇	—	4	8	no	—
450	C₂×C₄×C₆₇	—	4	4	no	—
451	C₂×C₄×C₆₇	—	4	4	no	—
452	C₂×C₄×C₆₇	—	8	4	no	—
453	C₂×C₄×C₆₇	—	8	4	no	—
454	C₂×C₄×C₆₇	—	8	4	no	—
455	C₂×C₄×C₆₇	—	8	4	no	—
456	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
457	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
458	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
459	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
460	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
461	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
462	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
463	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
464	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
465	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
466	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
467	C₂²×C₆₇	—	2	2	no	—
468	C₂²×C₆₇	—	2	2	no	—
469	C₂²×C₆₇	—	2	2	no	—
470	C₂²×C₆₇	—	2	2	no	—
471	C₂²×C₆₇	—	2	2	no	—
472	C₂²×C₆₇	—	2	2	no	—
473	C₂²×C₆₇	—	2	2	no	—
474	C₂²×C₆₇	—	2	2	no	—
475	C₂²×C₆₇	—	2	4	no	—
476	C₂²×C₆₇	—	2	4	no	—
477	C₂²×C₆₇	—	2	4	no	—
478	C₂²×C₆₇	—	2	2	no	—
479	C₂²×C₆₇	—	4	2	no	—
480	C₂²×C₆₇	—	4	1	no	—
481	C₂²×C₆₇	—	4	1	no	—
482	C₂²×C₆₇	—	4	2	no	—
483	C₂²×C₆₇	—	4	1	no	—
484	C₂²×C₆₇	—	4	2	no	—
485	C₂²×C₆₇	—	4	1	no	—
486	C₂²×C₆₇	—	4	2	no	—
487	C₂²×C₆₇	#520	1	4	yes	—
488	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
489	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
490	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
491	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
492	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
493	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
494	C₂²×C₆₇	#585	1	1	yes	characteristic
495	C₄×C₆₇	—	2	2	no	—
496	C₄×C₆₇	—	2	2	no	—
497	C₄×C₆₇	—	2	4	no	—
498	C₄×C₆₇	—	2	2	no	—
499	C₄×C₆₇	—	2	2	no	—
500	C₄×C₆₇	—	2	4	no	—
501	C₄×C₆₇	—	2	4	no	—
502	C₄×C₆₇	—	2	2	no	—
503	C₄×C₆₇	—	4	1	no	—
504	C₄×C₆₇	—	4	1	no	—
505	C₄×C₆₇	—	4	2	no	—
506	C₄×C₆₇	—	4	2	no	—
507	C₄×C₆₇	—	4	2	no	—
508	C₄×C₆₇	—	4	1	no	—
509	C₄×C₆₇	—	4	1	no	—
510	C₄×C₆₇	—	4	1	no	—
511	C₄×C₆₇	—	4	1	no	—
512	C₄×C₆₇	—	4	1	no	—
513	C₄×C₆₇	—	4	2	no	—
514	C₄×C₆₇	#520	1	4	yes	—
515	#34461	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
516	C₂×C₆₇	—	2	4	no	—
517	C₂×C₆₇	—	4	2	no	—
518	C₂×C₆₇	—	4	4	no	—
519	C₂×C₆₇	C₂×#520	1	1	yes	characteristic
520	C₂×C₆₇	C₂×#520	1	1	yes	characteristic
521	C₂×C₆₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
522	C₂×C₆₇	#3537	1	1	yes	characteristic
523	C₂×C₆₇	#3541	1	1	yes	characteristic
524	C₂×C₆₇	#3552	1	1	yes	characteristic
525	C₂×C₆₇	#3559	1	1	yes	characteristic
526	C₂×#553	C₂×C₆₇	1	1	yes	characteristic
527	#2383	C₂×C₆₇	1	2	yes	complemented
528	#2376	C₂×C₆₇	1	2	yes	complemented
529	#2370	C₂×C₆₇	1	1	yes	characteristic, complemented
530	#2361	C₂×C₆₇	1	1	yes	characteristic, complemented
531	#2361	C₂×C₆₇	1	2	yes	complemented
532	#2361	C₂×C₆₇	1	1	yes	characteristic, complemented
533	D₄×C₄⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
534	D₄×C₄⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
535	D₄×C₄⋊C₄	C₂×C₆₇	1	2	yes	complemented
536	#2347	C₂×C₆₇	1	1	yes	characteristic, complemented
537	#2345	C₂×C₆₇	1	1	yes	characteristic, complemented
538	#2334	C₂×C₆₇	1	2	yes	complemented
539	#2330	C₂×C₆₇	1	1	yes	characteristic, complemented
540	#2325	C₂×C₆₇	1	2	yes	complemented
541	#2324	C₂×C₆₇	1	1	yes	characteristic, complemented
542	#2322	C₂×C₆₇	1	2	yes	complemented
543	#2319	C₂×C₆₇	1	1	yes	characteristic, complemented
544	#2318	C₂×C₆₇	1	2	yes	complemented
545	#2317	C₂×C₆₇	1	1	yes	characteristic, complemented
546	C₄×#121	C₂×C₆₇	1	1	yes	characteristic, complemented
547	C₂×#389	C₂×C₆₇	1	1	yes	characteristic, complemented
548	#2290	C₂×C₆₇	1	1	yes	characteristic, complemented
549	C₆₇	#34461	1	1	yes	characteristic, direct product factor, Sylow
550	#553	C₄×C₆₇	1	16	yes	complemented
551	C₂×#126	C₂²×C₆₇	1	2	yes	—
552	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
553	C₂×#123	C₂²×C₆₇	1	2	yes	—
554	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
555	C₂×#121	C₂²×C₆₇	1	2	yes	—
556	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
557	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
558	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
559	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
560	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
561	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
562	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
563	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
564	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
565	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
566	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
567	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
568	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
569	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
570	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
571	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
572	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
573	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
574	#390	C₂²×C₆₇	1	1	yes	characteristic
575	#390	C₂²×C₆₇	1	1	yes	characteristic
576	#390	C₂²×C₆₇	1	2	yes	—
577	#389	C₂²×C₆₇	1	1	yes	characteristic
578	#389	C₂²×C₆₇	1	1	yes	characteristic
579	#389	C₂²×C₆₇	1	1	yes	characteristic
580	#389	C₂²×C₆₇	1	1	yes	characteristic
581	#389	C₂²×C₆₇	1	1	yes	characteristic
582	#389	C₂²×C₆₇	1	2	yes	—
583	#389	C₂²×C₆₇	1	2	yes	—
584	#389	C₂²×C₆₇	1	1	yes	characteristic
585	#389	C₂²×C₆₇	1	2	yes	—
586	#389	C₂²×C₆₇	1	2	yes	—
587	#389	C₂²×C₆₇	1	2	yes	—
588	#389	C₂²×C₆₇	1	1	yes	characteristic
589	#389	C₂²×C₆₇	1	1	yes	characteristic
590	#389	C₂²×C₆₇	1	2	yes	—
591	#388	C₂²×C₆₇	1	2	yes	—
592	#388	C₂²×C₆₇	1	2	yes	—
593	#388	C₂²×C₆₇	1	2	yes	—
594	#388	C₂²×C₆₇	1	2	yes	—
595	#388	C₂²×C₆₇	1	1	yes	characteristic
596	#388	C₂²×C₆₇	1	2	yes	—
597	#388	C₂²×C₆₇	1	2	yes	—
598	#388	C₂²×C₆₇	1	2	yes	—
599	#388	C₂²×C₆₇	1	1	yes	characteristic
600	#388	C₂²×C₆₇	1	2	yes	—
601	#387	C₂²×C₆₇	1	2	yes	—
602	#387	C₂²×C₆₇	1	2	yes	—
603	#387	C₂²×C₆₇	1	2	yes	—
604	#387	C₂²×C₆₇	1	2	yes	—
605	#387	C₂²×C₆₇	1	2	yes	—
606	#387	C₂²×C₆₇	1	1	yes	characteristic
607	#387	C₂²×C₆₇	1	2	yes	—
608	#387	C₂²×C₆₇	1	1	yes	characteristic
609	#386	C₂²×C₆₇	1	2	yes	—
610	#386	C₂²×C₆₇	1	2	yes	—
611	#386	C₂²×C₆₇	1	2	yes	—
612	#386	C₂²×C₆₇	1	1	yes	characteristic
613	#386	C₂²×C₆₇	1	2	yes	—
614	#386	C₂²×C₆₇	1	1	yes	characteristic
615	#385	C₂²×C₆₇	1	2	yes	—
616	#385	C₂²×C₆₇	1	2	yes	—
617	#385	C₂²×C₆₇	1	1	yes	characteristic
618	#385	C₂²×C₆₇	1	2	yes	—
619	#385	C₂²×C₆₇	1	2	yes	—
620	#385	C₂²×C₆₇	1	2	yes	—
621	#385	C₂²×C₆₇	1	2	yes	—
622	#385	C₂²×C₆₇	1	2	yes	—
623	#385	C₂²×C₆₇	1	2	yes	—
624	#385	C₂²×C₆₇	1	2	yes	—
625	#385	C₂²×C₆₇	1	1	yes	characteristic
626	#384	C₂²×C₆₇	1	2	yes	—
627	#384	C₂²×C₆₇	1	1	yes	characteristic
628	#383	C₂²×C₆₇	1	2	yes	—
629	#382	C₂²×C₆₇	1	2	yes	—
630	#381	C₂²×C₆₇	1	2	yes	—
631	#380	C₂²×C₆₇	1	2	yes	—
632	#380	C₂²×C₆₇	1	2	yes	—
633	#380	C₂²×C₆₇	1	1	yes	characteristic
634	#380	C₂²×C₆₇	1	2	yes	—
635	#380	C₂²×C₆₇	1	1	yes	characteristic
636	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
637	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
638	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
639	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
640	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
641	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
642	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
643	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
644	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
645	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
646	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
647	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
648	#376	C₂²×C₆₇	1	1	yes	characteristic
649	C₂×#95	C₂²×C₆₇	1	2	yes	—
650	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
651	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
652	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
653	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
654	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
655	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
656	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
657	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
658	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
659	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
660	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
661	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
662	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
663	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
664	#126	C₂×C₄×C₆₇	1	16	yes	complemented
665	#125	C₂×C₄×C₆₇	1	8	yes	complemented
666	#123	C₂×C₄×C₆₇	1	16	yes	complemented
667	#121	C₂×C₄×C₆₇	1	16	yes	complemented
668	#121	C₂×C₄×C₆₇	1	8	yes	complemented
669	#121	C₂×C₄×C₆₇	1	8	yes	complemented
670	C₄×D₄	—	4	2	no	—
671	C₄×D₄	—	4	2	no	—
672	C₄×D₄	—	4	4	no	—
673	C₄×D₄	—	4	4	no	—
674	C₄×D₄	—	4	4	no	—
675	C₄×D₄	—	4	4	no	—
676	C₄×D₄	C₂×C₄×C₆₇	1	16	yes	complemented
677	C₄×D₄	C₂×C₄×C₆₇	1	8	yes	complemented
678	C₄×D₄	C₂×C₄×C₆₇	1	8	yes	complemented
679	#117	—	4	2	no	—
680	#117	C₂×C₄×C₆₇	1	8	yes	complemented
681	C₂×C₄⋊C₄	—	4	4	no	—
682	C₂×C₄⋊C₄	—	4	2	no	—
683	C₂×C₄⋊C₄	—	4	2	no	—
684	C₂×C₄⋊C₄	—	4	4	no	—
685	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	8	yes	complemented
686	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
687	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
688	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
689	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
690	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
691	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
692	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
693	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
694	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
695	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
696	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
697	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
698	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
699	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
700	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
701	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
702	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
703	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
704	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
705	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
706	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
707	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
708	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
709	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
710	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
711	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
712	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
713	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
714	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
715	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
716	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
717	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
718	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
719	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
720	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
721	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
722	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
723	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
724	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
725	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
726	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
727	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
728	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
729	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
730	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
731	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
732	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
733	C₂×C₄²	—	4	2	no	—
734	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
735	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
736	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
737	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
738	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
739	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
740	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
741	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
742	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
743	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
744	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
745	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
746	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
747	#95	C₂³×C₆₇	1	2	yes	—
748	#95	C₂³×C₆₇	1	2	yes	—
749	#95	C₂³×C₆₇	1	2	yes	—
750	#95	C₂³×C₆₇	1	2	yes	—
751	#95	C₂³×C₆₇	1	1	yes	characteristic
752	#95	C₂³×C₆₇	1	1	yes	characteristic
753	#95	C₂³×C₆₇	1	1	yes	characteristic
754	#95	C₂³×C₆₇	1	1	yes	characteristic
755	#95	C₂³×C₆₇	1	1	yes	characteristic
756	#95	C₂³×C₆₇	1	2	yes	—
757	#95	C₂³×C₆₇	1	2	yes	—
758	#95	C₂³×C₆₇	1	2	yes	—
759	#95	C₂³×C₆₇	1	2	yes	—
760	#95	C₂³×C₆₇	1	1	yes	characteristic
761	#95	C₂³×C₆₇	1	1	yes	characteristic
762	#95	C₂³×C₆₇	1	1	yes	characteristic
763	#95	C₂³×C₆₇	1	1	yes	characteristic
764	#95	C₂³×C₆₇	1	2	yes	—
765	#95	C₂³×C₆₇	1	2	yes	—
766	#95	C₂³×C₆₇	1	2	yes	—
767	#95	C₂³×C₆₇	1	2	yes	—
768	#95	C₂³×C₆₇	1	2	yes	—
769	#95	C₂³×C₆₇	1	2	yes	—
770	#95	C₂³×C₆₇	1	2	yes	—
771	#95	C₂³×C₆₇	1	1	yes	characteristic
772	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
773	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
774	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
775	C₂×D₄	—	2	4	no	—
776	C₂×D₄	—	2	2	no	—
777	C₂×D₄	—	2	2	no	—
778	C₂×D₄	—	2	4	no	—
779	C₂×D₄	—	2	2	no	—
780	C₂×D₄	—	2	2	no	—
781	C₂×D₄	—	4	2	no	—
782	C₂×D₄	—	4	2	no	—
783	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
784	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
785	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
786	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
787	C₂²×C₄	—	2	2	no	—
788	C₂²×C₄	—	2	2	no	—
789	C₂²×C₄	—	2	2	no	—
790	C₂²×C₄	—	2	2	no	—
791	C₂²×C₄	—	2	2	no	—
792	C₂²×C₄	—	2	2	no	—
793	C₂²×C₄	—	2	4	no	—
794	C₂²×C₄	—	2	2	no	—
795	C₂²×C₄	—	2	4	no	—
796	C₂²×C₄	—	4	1	no	—
797	C₂²×C₄	—	4	1	no	—
798	C₂²×C₄	—	4	2	no	—
799	C₂²×C₄	—	4	2	no	—
800	C₂²×C₄	—	4	2	no	—
801	C₂²×C₄	—	4	2	no	—
802	C₂²×C₄	—	4	1	no	—
803	C₂²×C₄	—	4	2	no	—
804	C₂²×C₄	—	4	2	no	—
805	C₂²×C₄	—	4	2	no	—
806	C₂²×C₄	—	4	2	no	—
807	C₂²×C₄	—	4	2	no	—
808	C₂²×C₄	—	4	2	no	—
809	C₂²×C₄	—	4	2	no	—
810	C₂²×C₄	—	4	2	no	—
811	C₂²×C₄	—	4	2	no	—
812	C₂²×C₄	—	4	2	no	—
813	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
814	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
815	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
816	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
817	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
818	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
819	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
820	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
821	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
822	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
823	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
824	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
825	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
826	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
827	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
828	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
829	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
830	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
831	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
832	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
833	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
834	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
835	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
836	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
837	C₄⋊C₄	—	2	2	no	—
838	C₄⋊C₄	—	2	4	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	4	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	—	4	2	no	—
845	C₄⋊C₄	—	4	2	no	—
846	C₄⋊C₄	—	4	2	no	—
847	C₄⋊C₄	—	4	2	no	—
848	C₄⋊C₄	—	4	2	no	—
849	C₄⋊C₄	—	4	2	no	—
850	C₄⋊C₄	—	4	1	no	—
851	C₄⋊C₄	—	4	1	no	—
852	C₄⋊C₄	—	4	2	no	—
853	C₄⋊C₄	—	4	2	no	—
854	C₄⋊C₄	—	4	2	no	—
855	C₄⋊C₄	—	4	1	no	—
856	C₄⋊C₄	—	4	2	no	—
857	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
858	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
859	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
860	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
861	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
862	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
863	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
864	C₂²⋊C₄	—	2	2	no	—
865	C₂²⋊C₄	—	2	4	no	—
866	C₂²⋊C₄	—	2	2	no	—
867	C₂²⋊C₄	—	2	2	no	—
868	C₂²⋊C₄	—	4	1	no	—
869	C₂²⋊C₄	—	4	1	no	—
870	C₂²⋊C₄	—	4	2	no	—
871	C₂²⋊C₄	—	4	2	no	—
872	C₂²⋊C₄	—	4	2	no	—
873	C₂²⋊C₄	—	4	2	no	—
874	C₂²⋊C₄	—	4	2	no	—
875	C₂²⋊C₄	—	4	2	no	—
876	C₂²⋊C₄	—	4	2	no	—
877	C₂²⋊C₄	—	4	1	no	—
878	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
879	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
880	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
881	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
882	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
883	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
884	C₄²	—	2	2	no	—
885	C₄²	—	2	2	no	—
886	C₄²	—	2	2	no	—
887	C₄²	—	2	2	no	—
888	C₄²	—	4	1	no	—
889	C₄²	—	4	1	no	—
890	C₄²	—	4	2	no	—
891	C₄²	—	4	2	no	—
892	C₄²	—	4	2	no	—
893	C₄²	—	4	2	no	—
894	C₄²	—	4	2	no	—
895	C₄²	C₂²×C₄×C₆₇	1	8	yes	—
896	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
897	C₂³	—	2	1	no	—
898	C₂³	—	2	1	no	—
899	C₂³	—	2	1	no	—
900	C₂³	—	2	1	no	—
901	C₂³	—	2	1	no	—
902	C₂³	—	2	1	no	—
903	C₂³	—	2	2	no	—
904	C₂³	—	2	2	no	—
905	C₂³	—	2	1	no	—
906	C₂³	—	2	2	no	—
907	C₂³	—	2	1	no	—
908	C₂³	—	2	1	no	—
909	C₂³	—	2	2	no	—
910	C₂³	—	2	2	no	—
911	C₂³	—	2	2	no	—
912	C₂³	—	2	1	no	—
913	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
914	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
915	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
916	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
917	C₂³	2₋¹⁺⁴×C₆₇	1	2	yes	—
918	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
919	D₄	—	2	16	no	—
920	D₄	—	2	8	no	—
921	D₄	—	2	8	no	—
922	D₄	—	4	8	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	8	no	—
940	C₂×C₄	—	2	8	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	1	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	1	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	2	1	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	1	no	—
972	C₂×C₄	—	2	1	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	4	8	no	—
975	C₂×C₄	—	4	8	no	—
976	C₂×C₄	—	4	4	no	—
977	C₂×C₄	—	4	4	no	—
978	C₂×C₄	—	8	4	no	—
979	C₂×C₄	—	8	4	no	—
980	C₂×C₄	—	8	4	no	—
981	C₂×C₄	—	8	4	no	—
982	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
983	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
984	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
985	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
986	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
987	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
988	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
989	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
990	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
991	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
992	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
993	C₂²	—	2	2	no	—
994	C₂²	—	2	2	no	—
995	C₂²	—	2	2	no	—
996	C₂²	—	2	2	no	—
997	C₂²	—	2	2	no	—
998	C₂²	—	2	2	no	—
999	C₂²	—	2	2	no	—
1000	C₂²	—	2	2	no	—
1001	C₂²	—	2	4	no	—
1002	C₂²	—	2	4	no	—
1003	C₂²	—	2	4	no	—
1004	C₂²	—	2	2	no	—
1005	C₂²	—	4	2	no	—
1006	C₂²	—	4	1	no	—
1007	C₂²	—	4	1	no	—
1008	C₂²	—	4	2	no	—
1009	C₂²	—	4	1	no	—
1010	C₂²	—	4	2	no	—
1011	C₂²	—	4	1	no	—
1012	C₂²	—	4	2	no	—
1013	C₂²	#520×C₆₇	1	4	yes	—
1014	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
1015	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1016	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1017	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1018	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
1019	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
1020	C₂²	#585×C₆₇	1	1	yes	characteristic
1021	C₄	—	2	2	no	—
1022	C₄	—	2	2	no	—
1023	C₄	—	2	2	no	—
1024	C₄	—	2	4	no	—
1025	C₄	—	2	2	no	—
1026	C₄	—	2	2	no	—
1027	C₄	—	2	4	no	—
1028	C₄	—	2	4	no	—
1029	C₄	—	4	1	no	—
1030	C₄	—	4	1	no	—
1031	C₄	—	4	2	no	—
1032	C₄	—	4	2	no	—
1033	C₄	—	4	2	no	—
1034	C₄	—	4	1	no	—
1035	C₄	—	4	1	no	—
1036	C₄	—	4	1	no	—
1037	C₄	—	4	1	no	—
1038	C₄	—	4	1	no	—
1039	C₄	—	4	2	no	—
1040	C₄	#520×C₆₇	1	4	yes	—
1041	C₂	—	2	4	no	—
1042	C₂	—	4	2	no	—
1043	C₂	—	4	4	no	—
1044	C₂	C₂×#520×C₆₇	1	1	yes	characteristic
1045	C₂	C₂×#520×C₆₇	1	1	yes	characteristic
1046	C₂	C₄×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1047	C₂	C₆₇×#3537	1	1	yes	characteristic
1048	C₂	C₆₇×#3541	1	1	yes	characteristic
1049	C₂	C₆₇×#3552	1	1	yes	characteristic
1050	C₂	C₆₇×#3559	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂×#553×C₆₇	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₆₇×#2383	C₂	semidirect
3. C₆₇×#2376	C₂	semidirect
4. C₆₇×#2370	C₂	semidirect
5. C₆₇×#2361	C₂	semidirect
6. C₆₇×#2361	C₂	semidirect
7. C₆₇×#2361	C₂	semidirect
8. D₄×C₄⋊C₄×C₆₇	C₂	semidirect
9. D₄×C₄⋊C₄×C₆₇	C₂	semidirect
10. D₄×C₄⋊C₄×C₆₇	C₂	semidirect
11. C₆₇×#2347	C₂	semidirect
12. C₆₇×#2345	C₂	semidirect
13. C₆₇×#2334	C₂	semidirect
14. C₆₇×#2330	C₂	semidirect
15. C₆₇×#2325	C₂	semidirect
16. C₆₇×#2324	C₂	semidirect
17. C₆₇×#2322	C₂	semidirect
18. C₆₇×#2319	C₂	semidirect
19. C₆₇×#2318	C₂	semidirect
20. C₆₇×#2317	C₂	semidirect
21. C₄×#121×C₆₇	C₂	semidirect
22. C₂×#389×C₆₇	C₂	semidirect
23. C₆₇×#2290	C₂	semidirect
24. #553×C₆₇	C₄	semidirect
138. #126×C₆₇	C₂×C₄	semidirect
139. #125×C₆₇	C₂×C₄	semidirect
140. #123×C₆₇	C₂×C₄	semidirect
141. #121×C₆₇	C₂×C₄	semidirect
142. #121×C₆₇	C₂×C₄	semidirect
143. #121×C₆₇	C₂×C₄	semidirect
150. C₄×D₄×C₆₇	C₂×C₄	semidirect
151. C₄×D₄×C₆₇	C₂×C₄	semidirect
152. C₄×D₄×C₆₇	C₂×C₄	semidirect
154. #117×C₆₇	C₂×C₄	semidirect
159. C₂×C₄⋊C₄×C₆₇	C₂×C₄	semidirect
515. #34461	C₆₇	direct (N × H)
527. #2383	C₂×C₆₇	semidirect
528. #2376	C₂×C₆₇	semidirect
529. #2370	C₂×C₆₇	semidirect
530. #2361	C₂×C₆₇	semidirect
531. #2361	C₂×C₆₇	semidirect
532. #2361	C₂×C₆₇	semidirect
533. D₄×C₄⋊C₄	C₂×C₆₇	semidirect
534. D₄×C₄⋊C₄	C₂×C₆₇	semidirect
535. D₄×C₄⋊C₄	C₂×C₆₇	semidirect
536. #2347	C₂×C₆₇	semidirect
537. #2345	C₂×C₆₇	semidirect
538. #2334	C₂×C₆₇	semidirect
539. #2330	C₂×C₆₇	semidirect
540. #2325	C₂×C₆₇	semidirect
541. #2324	C₂×C₆₇	semidirect
542. #2322	C₂×C₆₇	semidirect
543. #2319	C₂×C₆₇	semidirect
544. #2318	C₂×C₆₇	semidirect
545. #2317	C₂×C₆₇	semidirect
546. C₄×#121	C₂×C₆₇	semidirect
547. C₂×#389	C₂×C₆₇	semidirect
548. #2290	C₂×C₆₇	semidirect
549. C₆₇	#34461	direct (N × H)
550. #553	C₄×C₆₇	semidirect
664. #126	C₂×C₄×C₆₇	semidirect
665. #125	C₂×C₄×C₆₇	semidirect
666. #123	C₂×C₄×C₆₇	semidirect
667. #121	C₂×C₄×C₆₇	semidirect
668. #121	C₂×C₄×C₆₇	semidirect
669. #121	C₂×C₄×C₆₇	semidirect
676. C₄×D₄	C₂×C₄×C₆₇	semidirect
677. C₄×D₄	C₂×C₄×C₆₇	semidirect
678. C₄×D₄	C₂×C₄×C₆₇	semidirect
680. #117	C₂×C₄×C₆₇	semidirect
685. C₂×C₄⋊C₄	C₂×C₄×C₆₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#553×C₆₇	2
C₆₇×#2383	2
C₆₇×#2376	2
C₆₇×#2370	2
C₆₇×#2361	2
D₄×C₄⋊C₄×C₆₇	2
C₆₇×#2347	2
C₆₇×#2345	2
C₆₇×#2334	2
C₆₇×#2330	2
C₆₇×#2325	2
C₆₇×#2324	2
C₆₇×#2322	2
C₆₇×#2319	2
C₆₇×#2318	2
C₆₇×#2317	2
C₄×#121×C₆₇	2
C₂×#389×C₆₇	2
C₆₇×#2290	2
#34461	67

Subgroups — C67×#34461 #30713712

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34461 #30713712